Atmospheric Electricity - Ultra and Extremely Low Frequency Electromagnetic Fields - page 75

Fig. 3.15 ThesameasinFig. 3.4 but for thunderstorm QE field preceding BJ discharge (Surkov
and Hayakawa 2012 )
discharge size L such as discharge tube length, streamer radius and etc. scales
as L / n m / exp . z =H a /. Typical time interval T such as relaxation time,
mean free time between collisions, two-body attachment time and etc. scales as
T / n m . The typical velocity V / L=T whence it follows that the streamer
velocity, electron drift velocity V d , and so on are independent of n m whereas the
electron mobility V d =E c / n m . Plasma and charge density inside the streamer
body follows the scaling law: n e D n i / n 2 m while the plasma conductivity scales
as en e V d / n m .
The increase in streamer size with altitude predicted by the scaling theory is
compatible with the BJ observations. Although the similarity law for leader does
not exist (Raizer 1991 ), with some care one may speculate that the conical shape of
BJs and GJs (see Fig. 3.14 ) follows this similarity law since the scale of individual
streamers and of the whole streamer zone has to increase with height. However,
our calculations have demonstrated that the electric field produced by thundercloud
charges is still smaller than that required for propagation of positive streamer
(Fig. 3.15 ). Reasonable guesses as to the electrical inhomogeneity need to start
breakdown ionization of the air. Another way of explaining this contradiction has
been proposed by Raizer et al. ( 2006 , 2007 ). In their model the BJ can be resulted
from a bidirectional uncharged leader which in turn originates in the thundercloud
area where the electric field reaches a maximum value. Owing to the exponential
profile of the air density, the leader and the streamer corona are assumed to grow